Can you have a pet if you’re allergic?

We feel sorry for pet lovers with allergies, the bf being one of them. He'd love to have a dog but we can't figure out how this could ever be a happy scenario. Could we have a dog that lived outside? Or keep it to one room? But where's the fun if you can't snuggle up with your furry friend on the couch every now and then. So the question is, can you keep a pet if you have allergies?

If you are a pet owner living with allergies – how have you made it work?